DECAY OF VORTEX VELOCITY AND DIFFUSION OF TEMPERATURE IN A GENERALIZED SECOND GRADE FLUID

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid was introduced. The velocity and temperature fields of the vortex flow of a generalized second fluid with fractional derivative model were described by fractional partial differential equations. Exact analytical solutions of these differential equations were obtained by using the discrete Laplace transform of the sequential fractional derivatives and generalized Mittag-Leffler function. The influence of fractional coefficient on the decay of vortex velocity and diffusion of temperature was also analyzed.

广义二阶流体涡流速度的衰减和温度扩散

将分数阶微积分运算引入到二阶流体的本构关系中,建立了带分数阶导数的广义二阶流体模型· 研究了广义二阶流体涡流速度的衰减和温度扩散,利用分数阶导数的Laplace变换和广义Mittag＿Leffler函数,得到了涡流速度场和温度场的精确解。